results in the form of integral

i wrote this code:

clc

clear all

close all

%--------------------------------------------------------------------------

syms Alpha1 Betta2 Betta1 S1 S2 h q S

syms t R m h Etta H Et1 K STRu STRy n STRp Strc STRpc Et2 E_foam

%_________________

Gamma0=2*n*h*Etta;

Alpha01=acos(m);

Betta02=acos(1-m);

STR0=sqrt((STRy*STRu)/(1+K));

Mp=(STR0*(t^2))/4;

Np=STR0*t;

%________________________________________________________

E_foam=(pi*((R-(t/2))^2)*int((Et1*(S/H)+STRp),S,0,2*n*h*Etta))

%___________________________________________________________________________________________________

Eb=(4*pi*Mp)*(((R+(m*h))*acos(m))+(h*sqrt(1-m^2))+(R*asin(1-m))+((R-(h*(1-m)))*acos(1-m)+R*asin(m)))

%_______________

Em=2*pi*Np*(h)^2

%______________________________________________________________________________

PART1=(Et1*(((S1*cos(Alpha1))-(m*h))/R)+STRp)*(2*pi)*(R-(S1*cos(Alpha1)+(m*h)));

Eint_AB1=int(int((-S1*PART1),S1,(m*h)/cos(Alpha1),h),Alpha1,Alpha01,0)

%________________________________________________________________

PART2=(Et1*((S1*cos(Betta1))/R)+STRp)*(2*pi)*(R-(S1*cos(Betta1)));

Eint_BC1=int(int((-S1*PART2),S1,0,h),Betta1,pi/2,Betta02)

%____________________________________________________________________________________

PART3=(Et1*((((1-m)*h)-S2*cos(Betta2))/R)+STRp)*(2*pi)*(R-(S2*cos(Betta2))-((1-m)*h));

Eint_BC2=int(int((-S2*PART3),S2,0,((1-m)*h)/cos(Betta2)),Betta2,Betta02,0)

%______________________________________________

E_int=Eint_AB1+Eint_BC1+Eint_BC2

the answers that i get from matlab are in the form of integral .the results are as followed:

Eint_AB1 =

int(-(h^2*pi*(m - cos(Alpha1))*(3*Et1*h^2*cos(Alpha1)^3 - 3*Et1*h^2*m^3 - 6*R^2*STRp*cos(Alpha1) - 6*R^2*STRp*m + 2*Et1*R*h*m^2 + 10*R*STRp*h*m^2 - 4*Et1*R*h*cos(Alpha1)^2 + 4*R*STRp*h*cos(Alpha1)^2 + 3*Et1*h^2*m*cos(Alpha1)^2 - 3*Et1*h^2*m^2*cos(Alpha1) + 2*Et1*R*h*m*cos(Alpha1) + 10*R*STRp*h*m*cos(Alpha1)))/(6*R*cos(Alpha1)^2), Alpha1, acos(m), 0)

Eint_BC1 =

(2*STRp*h^3*pi*((1 - (m - 1)^2)^(1/2) - 1))/3 - (2*Et1*h^3*pi*((1 - (m - 1)^2)^(1/2) - 1))/3 + R*STRp*h^2*pi*(pi/2 - acos(1 - m)) - (Et1*h^4*pi*(pi/4 - acos(1 - m)/2 + (m*(1 - (m - 1)^2)^(1/2))/2 - (1 - (m - 1)^2)^(1/2)/2))/(2*R)

Eint_BC2 =

int(-(h^2*pi*(m - 1)^2*(6*R^2*STRp - 3*Et1*h^2 - 3*Et1*h^2*m^2 + 2*Et1*R*h - 10*R*STRp*h + 6*Et1*h^2*m - 2*Et1*R*h*m + 10*R*STRp*h*m))/(6*R*cos(Betta2)^2), Betta2, acos(1 - m), 0)

as you can see the results of Eint_AB1 and Eint_BC2 are in the form of integrals.how can i solve this problem? i need the answers to not be in form of integrals and i want the results of this integrals.what sould i do?

thanks.

Answer 1

[John D'Errico]

Just wanting a result from some computation to have an analytical solution is not enough. Sometimes it requires additional mathematics, or a transformation applied. But much of the time, there simply is no analytical solution, no matter how much magic you apply.

If you knew the values of these many constants in there, you could supply them, and then perform a numerical integration, using either vpaintegral or integral. However, as long as there are symbolic, unknown constants involved, it is likely you will find no solution.

So sorry, need is not enough. If it were, many people around the world who were starving would now have full stomachs.